In several applications, high-speed switching drive mechanisms are connected to motors through long cables. For example, high power transistors have been used in variable speed drives to achieve high switching speeds and high frequency excitation of wiring connecting to motors. Because the cables have a defined physical length, electrical signals require a finite time to traverse the cables. If this time becomes appreciable relative to the time of one cycle of the exciting voltage, transmission line effects begin to appear on the cables. Even a small length of motor wiring in conduit can exhibit transient overvoltages at the motor due to wave reflections when it is driven by a PWM inverter, for example. The same kind of problems can arise in offshore pump motors supplied through several kilometers of undersea cable, even though the switching speeds may not be especially high.
As a more specific example, actuators may be interconnected to a control plant through long cables (e.g., transmission lines). If the actuator operates at a fast sampling rate (with respect to a propagation delay of the cable) and the actuator's impedance cannot be neglected, electromagnetic wave reflections will occur and transmitted pulses from the actuators will be deformed, degrading control quality. To overcome this problem, two techniques are often used. First, passive linear filters are often introduced to slow a rise time of the transmitted pulse. Unfortunately, this technique generally reduces the achievable bandwidth resulting in a below par performance.
A second solution is to match a load impedance of the control plant to an impedance of the long cables. Traveling waves can reflect back and forth along the line until they are ultimately damped out by transmission line losses. Using this solution, when the line is terminated in its characteristic impedance, there is no reflected wave and voltages and currents are generally uniform along the length of the line. Unfortunately, this approach can be difficult to realize since the choice of the filter parameters to match impedances is not obvious if the plant has nonlinear or uncertain characteristics.
The wave reflection phenomenon is well documented in power distribution and digital communications and is now coming to the forefront in several control applications. Notably, in high-performance drives it is known as a voltage overshoot problem, where the occurrence of high voltage spikes at motor terminals can produce potentially destructive stress on motor insulation, constituting a serious practical problem still asking for a satisfactory solution. (See, e.g., S. C. Lee and K. H. Nam, “An Overvoltage Suppression Scheme for AC Motor Drives Using a Half DC-Link Voltage Level at each PWM Transition”, IEEE Trans. Ind. Elec., Vol. 49, No. 3, pp. 549–557, June, 2002; and E. Persson, “Transient Effects in Application of PWM Inverters to Induction Motors”, IEEE Trans. Ind. Applicant., Vol. 28, No. 5, pp. 1095–1101, September/October, 1992).
Voltage overshoot occurs at the motor terminal if the motor is fed by a drive signal through a long feeding cable due to the transmission line behavior on the motor feeding cable. The driver is regarded as a short circuit because its impedance is low compared with the transmission line characteristic impedance. However, the motor impedance presents an effective open circuit. These impedance mismatches cause a voltage reflection that results in a voltage spike at the motor, and thereby constitutes a factor in the voltage overshoot phenomenon. Further, a signal propagation delay occurs in feeding cable transmission lines. If a signal rise time is short compared to the propagation delay, voltage overshoot takes place at the motor terminal, since reflection coefficients at both ends of the cable are normally high.